Skin effect on cables for harmonics study

[lume7006]

Dear fellows,

Currently, we are working on a harmonics study involving medium and low voltage network.
As in that network there have been some prrevious problems and some equipments were reported to be damaged, we are trying to
create a very detailed model based on the available information.

One of our points is related to modelling the cables frequency dependancy effects (skin effect among them), as well as in transformers.

We have seen that typically that is included using a sort of polinom that affects the 60 Hz values of resistance and reactance.
However, we have not found yet a good reference to be able to understand how to determine the constants of the polinom.

So, I am kindly requesting for some references (books, papers, or similar) that provide us information about this.

I thank you in advance

 

[LiteYear]

There are many, many resources on this topic, so it might be worthwhile narrowing your scope a little. Roughly speaking, skin effect means that resistance rises as frequency rises. Two other effects, inductance and capacitance, also affect the impedance as frequency rises. One way to model this would be with a curve fitting polynomial, but without seeing the polynomial you have, it's not possible to make much of a general statement.

Another way to model your cables and transformers is just as a collection of discrete resistors, inductors and capacitors, possibly with frequency dependant values. Solving the resulting equation may again result in a polynomial, the constants of which just fall out of the equation.

If there's a particular polynomial you're curious about, by all means post it and we can have a go at explaining it. Otherwise it's just a matter of studying basic circuit theory and developing the relevant equations yourself.

 

[Desrod2]

You might consider investing into a software with a detailed model. Also, since some equipment were damaged, there might be either unknown harmonic source(s) or resonance(s). Perform some field measurements.

Thinks of using experienced people. Harmonics are not easy to deal with.

 

[lume7006]

Thank you for your responses!

We already have a specialized software to do this fine modelling, and our question is related to know some references in order to learn to fill the fields.

For example, the software used has two possible equations:

1) k(f) = (1-a)+ a*(f/fnom)^b

2) k(f) = 1+a((f/fnom)-1))^b

The values we need are related to the constants identified as:
a and b.
They are to model the skin effect on cables and transformers.

Any help pointing some references in which we can read how these coefficients and equations are derived will be help!

 

[LiteYear]

I really don't think external references is the right place to start. Those formulas are very generic (though not polynomials) that look nothing like any skin effect formula I've ever seen. Your first port of call should be to the software manual that describes those equations. If you're stuck using those equations, you absolutely need to know what they represent before you can start putting them in terms of real values or physical phenomena.

 

[lume7006]

Hello,

We already looked at the software manual, however, there is no explanation about it or suggested values.

Software developer was already contacted and up to now, no response.

Because of that, we are trying to get some feedback from the engineering community who surely has been involved in something like this.

 

[LiteYear]

Fair enough. I wish you luck, but you might have been handed a hospital pass here.

For what it's worth, the typical derivation for skin effect goes like this:

δ=(ρ/(πfμ))^(1/2)

where:
[ul]
[li]δ - effective skin effect depth[/li]
[li]ρ - resistivity of the conductor[/li]
[li]f - frequency of the current[/li]
[li]μ - permeability of the conductor[/li]
[/ul]

Then you'll need to consider how the skin depth affects the resistance of the conductor. If you have a solid circular conductor of radius r, then the effective cross-sectional area for a given skin depth is:

A = πr[sup]2[/sup]-π(r-δ)[sup]2[/sup]
= π(2rδ - δ[sup]2[/sup])

And finally, the resistance of the conductor is found using:

R=ρl/A

Solve for R/l as a function of f and you get:

R/l (f) = ρ/(π(2r(ρ/(πfμ))^(1/2) - ρ/(πfμ)))

Assuming ρ, r and μ are constants and combining them into generic constants, you get:

R/l (f) = a/(bf[sup]-1/2[/sup] - cf[sup]-1[/sup])

As you can see, this doesn't look much like the equation you have, so I don't know what behaviour they're trying to model.

 

[Desrod2]

If equipment were damaged, I don't think that improving your model using skin effect will allow you to find out the source of your problem specially if your cables' impedance are very small compared to your load. You might want to try expanding your model on the supply side adding supply lines and substations (2 level up if possible). Check for capacitor banks at those substations and run a frequency scan. Once again I would recommend performing measurements for a relatively long period like a full week. Your installation might be getting harmonics from external sources and if you don't know that, even with the perfect model you won't be able to design proper mitigation. I have seen customers' filters damaged from external contributions.

 

[lume7006]

Dear fellows,

I thank you very much for your inputs, your different points of views as well as suggestions have been very good to us.

Regards,